Should I just quit Blender when after two weeks of learning and watching tutorials I cannot model anything?
Two weeks and you are thinking of quitting? No, no, no that will not do.
For anything even starting to be complex two weeks is just not enough time to call it quits. Learning takes time. How much time depends entirely on your effort. You have a good motivator to learn blender, to get into University. So do not loose sight of your goal.
Now how to go about that.
Stop watching tutorials. That's right, Stop watching tutorials. You said yourself that you &quot;forget everything and the things I've learned are just gone.&quot; (That is because you never actually learned them, you just saw some guy on youtube do something). I bet you have spent a fair bit of time watching tutorials. Look at the outcome, for you it is not worth it.
This is a common problem with tutorials. We watch all these tutorials, and feel great &quot;look at what I can do.&quot; Except if you just watch them, its nothing more then a movie. We feel like we conquered the world, but really we just sat on our butt for two hours.
So with tutorials out of the way, just make something. Start simple, such as the desk your sitting at. Yes it will be hard, your model will be pretty bad, and you will get stuck. However this is how you learn.
Ok so you are modeling, you hit a wall, no idea how to do X. Search for that thing (you very likely will get an answer from this site), then keep modeling.
It is ok to have to ask google how to do every step.
Here's the exciting part. You open blender up on day two, start by making another simple object. Say a wood stove. Now instead of having to search for everything you remembered that GG is edge slide, and why you should be moving that edge loop.

 Image from HomeDepo
Keep it up. Make something, anything every day. Keep it very simple. If you try to bite off more then you can do you will get discouraged and then it is easy to skip blender today, and down the spiral you fall.
Make a simple object everyday for a week and I guarantee you will learn more in that week then you have in all the time you spent in blender and watching tutorials up to this point.
Don't get discouraged when your models don't look like you wanted, or your renders aren't pretty. This is part of the learning process. I bet your first steps as a baby weren't too good either.
Please do not feel like you have to remember everything or every keyboard shortcut. Many times I have searched for something and found the answer, only to discover that I wrote the answer!

TLDR
Stop watching tutorials and just make stuff, mistakes included, in blender.